Question

Pls help

Simplify the logarithmic expression

Answer 1

9514 1404 393

Answer:

log₁₂(4)

Explanation:

The applicable rule of logarithms (to the same base) is ...

log(a^b) = b·log(a)

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Then the expression simplifies as follows:

`3\log_(12)(2)+(1)/(3)\log_(12)(2^3)-\log_(12)(2^2)\\\\=3\log_(12)(2)+(3)/(3)\log_(12)(2)-2\log_(12)(2)=(3+1-2)\log_(12)(2)\\\\=2\log_(12)(2)=\log_(12)(2^2)=\boxed{\log_(12)(4)}`